This book provides backgrounds and the mathematical methods necessary to understand the basic transforms in signal processing and linear systems to prepare for in depth study of analog and digital communications systems.
This tutorial presentation provides developments of Fourier series and other orthogonal series, including trigonometric and complex exponential Fourier series, least squares approximations and generalized Fourier series, and the spectral content of periodic signals.
This text thoroughly covers Fourier transform pairs for continuous time signals, Fourier transform properties, and the magnitude and phase of Fourier transforms.
The author includes discussions of techniques for the analysis of continuous time linear systems in the time and frequency domains with particular emphasis on the system transfer function, impulse response, system/filter bandwidth, power and energy calculations, and the time domain sampling theorem.
Author(s): Jerry D. Gibson
Series: Synthesis Lectures on Communications
Publisher: Springer
Year: 2023
Language: English
Pages: 160
City: Cham
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Binder1
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Contents
About the Author
978-3-031-19580-8_1
1 Orthogonal Functions and Fourier Series
1.1 Introduction
1.2 Signal Representation and Orthogonal Functions
1.3 Trigonometric Fourier Series
1.4 Exponential (Complex) Fourier Series
1.5 Fourier Coefficient Evaluation Using Special Properties
1.6 Least Squares Approximations and Generalized Fourier Series
1.7 Spectral Content of Periodic Signals
Summary
Problems
References
978-3-031-19580-8_2
2 Fourier Transforms
2.1 Introduction
2.2 Fourier Transform Pair
2.3 Existence of the Fourier Transform
2.4 Generalized Functions
2.5 Fourier Transforms and Impulse Functions
2.6 Fourier Transform Properties
2.7 Graphical Presentation of Fourier Transforms
Summary
Problems
References
978-3-031-19580-8_3
3 Linear Systems, Convolution, and Filtering
3.1 Introduction
3.2 Linear Systems
3.3 Linear Systems Response: Convolution
3.4 Graphical Convolution
3.5 Ideal Filters
3.6 Physically Realizable Filters
3.7 Time-Domain Response and System Bandwidth
3.8 The Sampling Theorem
3.9 Power and Energy
Summary
Problems
References
978-3-031-19580-8_4
4 Random Variables and Stochastic Processes
4.1 Introduction
4.2 Probability
4.3 Probability Density and Distribution Functions
4.4 Mean, Variance, and Correlation
4.5 Transformations of Random Variables
4.6 Special Distributions
4.7 Stochastic Processes and Correlation
4.8 Ergodicity
4.9 Spectral Densities
4.10 Cyclostationary Processes
Summary
Problems
References
